President Jacques Chirac said after a meeting of ministers and advisers: "The Republic is quite determined, by definition, to be stronger than those who want to sow violence or fear. The law must have the last word."

Last night 10 policemen were injured, two of them seriously, when youths opened fire with a shotgun in the Essonne region south of Paris. In Saint-Etienne, southern France, youths seized a bus and ordered passengers to get off before torching the vehicle, injuring the driver and a passenger, while in eastern Strasbourg, rioters threw Molotov cocktails into a primary school, and in Toulouse, a car was pushed towards the entrance of a metro tunnel. Police said that at least 300 cars wereer torched and 37 people had been arrested across the country.

Saturday night's incidents in the centre of Paris, in which 32 cars were burnt and 30 youths arrested, marked a new and disturbing escalation after nearly two weeks of intensifying riots.

Almost 1,300 cars were burnt across France on Saturday night ­ a new record ­ as copycat riots by gangs of disaffected and criminal youths broke out in towns from the Belgian border to the Mediterranean coast, and from Alsace to Normandy.

The worst -hit provincial town was Evreux, in upper Normandy, where 100 youths fought with police. A shopping mall, a post office, two schools and 50 cars were destroyed by fire.

In the Paris suburbs, two nursery schools were burnt to the ground. A McDonald's restaurant and a gymnasium disappeared in flames after being rammed by blazing cars.

In Evry, south of Paris, police discovered a Molotov cocktail factory in a disused police station. Six teenagers were arrested. Sixty litres of petrol and 150 bottles, a third of them filled and ready to be used, were seized.

Small gangs of rioters entered the city of Paris for the first time on Saturday night and hurled petrol bombs at parked cars. Two of the attacks took place on the northern outskirts of the capital, and one gang set fire to half a dozen cars close to the offices of the Libération newspaper, near the Place de la République in the centre of the city. Despite the worst destruction since the riots began, a police spokesman called for a sense of proportion. He said: "It's 211 districts out of 36,000, so France is not burning."

The Prime Minister, Dominique de Villepin, said the government would step up security. A total of 2,300 extra officers had already been drafted in. " We cannot accept any 'no-go' areas," M. de Villepin said, adding that he would announce plans for the country's underprivileged suburbs on television today.

Police said they had been expecting small raids but thought serious outbreaks of violence in the capital were unlikely. The multiracial suburban gangs which are mostly responsible for the 12 days of rioting prefer to operate within their own territory where they are not so vulnerable to arrest, the police said.

For a beleaguered and muddled government, there were signs of hope at the weekend. In two Paris suburbs, young arsonists were seized by older residents and handed to the police: the first signs of a revolt against the revolt by people who are the primary victims of the riots.

People of all races and religions marched silently through three suburban towns on Saturday, calling for a return to calm and common sense. The parents of two teenage boys whose deaths sparked the original unrest in Clichy-sous-Bois, north-east of Paris, put out a moving and dignified statement. "We call for tempers to cool down and for an end to all violence and for a return to a sense of civic duty on all sides. France does not deserve this," said the families of Bouna Traore and Zyed Benna, who died after they climbed into an electricity sub-station to escape a police identity check.

It remains to be seen how far such appeals will influence the youths. Although the Interior Minister, Nicolas Sarkozy, has spoken darkly of " organisation" of the riots by drugs barons or Islamist radicals, police chiefs and social workers dismiss such claims. Police intelligence experts say that almost all of the violence is coming from known gangs, with help from other local youths, some as young as 10 or 12. There can be no co-ordination between the gangs in different cités (housing estates), they say, because they detest each other as much as they detest the police.

The Union of French Islamic Organisations issued a fatwa against rioting after officials suggested that Muslim militants could be partly to blame.

The violence is a statement of anger and rejection against mainstream French society but also reflects a determination by each local gang in the Paris suburbs ­ and now in disadvantaged quartiers across the nation ­ to have its night of bonfires and its name on the television news.

Weeks ago, M. Sarkozy talked of "cleaning out" the violent youth gangs with a Karcher, or high-powered hose. After the deaths in Clichy, he described the gangs as racaille, or scum. The youths setting fire to their own brothers' and sisters' schools, or their neighbours' cars, are part of a multiracial under-class of 15- to 22-year-olds whose only currencies are drugs and violence. They are determined to show M. Sarkozy that they will not be "cleaned out" so easily.

There were new calls over the weekend, from left-wing politicians and community leaders in the suburbs, for M. Sarkozy to resign. In an article in Le Monde, M. Sarkozy said he had no intention of doing so. If his approach failed, he said, the law of drugs barons and Islamists would prevail. An opinion poll in Le Parisien newspaper suggested M. Sarkozy remained popular.

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